I would favor Magneto a majority but It's an interesting (and somewhat open) question given each of The Mandarin's rings serve a very specific function and some of them in theory Magneto has little or no defence against.
The matter rearranging ring for example, the gravity/mass ring, or the Black light beam. Using his rings strategically Mandarin has every chance of countering and depleting Magneto, indeed if the encounter is on level ground and given Mandarin is very well educated in physics he may be able to neutralise Magneto's magnetic abilities enough for a one on one beatdown - if Mandarin gets any sort of chance to strike him no way is Magneto going to come out unscathed from someone who can physically damage Iron Man's armour with his bare hands...
It all comes down to circumstance and what the specifics are, but on average Magneto has more scope with his abilities and there is no reason to assume the Rings would be immune to Magneto's direct influence. In fact hasn't Iron Man used magnetism to draw them from Mandarin's fingers in the past? May be misremembering.
Your memory is perfect. Iron Man Vol.1 #100.